UC-NRLF 


T    C 
177 


B   H  fllM   SSfi 


1898 
ENGI 


EHGINE6&& 


California    Academy    of    Bclenoei 

Carl   Ewald  Grunsky  Bequest 
August  I,  1O34 


The 

Venturi 

Meter 


BUILDERS  IRON  FOUNDRY, 
PROVIDENCE,  R.  I.,  U.  S.  A. 
i 


The  Venturi  Meter 

AN  INSTRUMENT  MAKING  USE  OF  A  NEW  METHOD  OF 
GAUGING  WATER;  APPLICABLE  TO  THE  CASES  OF 
VERY  LARGE  TUBES,  AND  OF  A  SMALL  VALUE 

ONLY,    OF    THE    LIQUID    TO    BE    GAUGED. 
BY 

CLEMENS  HERSCHEL,  M.  Am.  Soc.  C.  E. 

Read  before  the  American  Society  of  Civil  Engineers, 
December  21,  1887. 


For  this  paper  the  American  Society  of  Civil  Engineers  awarded 
Mr.  Herschel  the  Rowland  Prize. 


REPRINTED  BY 


BUILDERS  IRON   FOUNDRY, 

PROVIDENCE,  R.  I. 

1898 


•-•• 


THE  VENTURI  METER 

AN  INSTRUMENT  MAKING  USE  OF  A  NEW  METHOD  OF 
GAUGING  WATER  ;  APPLICABLE  TO  THE  CASES  OF 
VERY  LARGE  TUBES,  AND  OF  A  SMALL  VALUE 
ONLY,  OF  THE  LIQUID  TO  BE  GAUGED. 


By  CLEMENS  HERSCHEL,  M.  Am.  Soc.  C.  E. 

READ  BEFORE  THE  AMERICAN  SOCIETY  OF  CIVIL  ENGINEERS 
DECEMBER  21  st,  1887. 


"Introduction;  analogy;  assumptions  founded  on  facts  and  unceasingly 
rectified  by  additional  observations :  a  genial  form  of  tact,  inborn,  but 
strengthening  itself  by  making  numerous  comparisons  between  its 
indications  and  the  results  of  experiment;  such  are  the  principal 
means  of  arriving  at  the  truth." — Laplace,  des  divers  moyens  d'approcher 
de  la  certitude. 

New  Meter  Some   additional   instrument   or   method   for   gauging 

water  has  long  been  desired  by  hydraulic  engineers.  In 
the  case  of  water  flowing  through  pipes,  as  in  city  water- 
works, it  is  extremely  difficult  or  impracticable  to  meter 
the  water,  as  soon  as  diameters  approaching  one  foot,  or 
quantities  approaching  one  million  gallons  daily,  are 
reached.  In  some  such  cases  the  stream  of  water  has 
been  split  up  into  many  smaller  ones,  each  of  which  was 
then  furnished  with  a  meter,  and  the  tail  water  of  these 
meters  reunited  —  a  method  and  apparatus  so  cumber- 


/cm 


CLEMENS  HERSCHEL'S  PAPER. 


some  and  costly  as  to  be  rarely  applicable.  Taking  the 
case,  on  the  other  hand,  of  a  far  less  valuable  commodity, 
viz.,  of  water  under  little  or  no  pressure,  about  to  be  or 
after  it  has  been  used  for  power,  the  practical  difficulties 
of  gauging  again  become  very  great.  Ordinary  meters 
are  out  of  the  question,  owing  to  the  small  value  of  the 
article  per  cubic  foot,  and  to  the  proportionately  great 
cost,  per  cubic  foot  of  water  metered,  of  applying  a 
mechanical  meter.  *  *  * 

It  has  long  seemed  to  the  writer  that  an  application  to 
metering  water  of  the  principle  involved  in  the  Bourdon 
anemometer,  an  instrument  which  has  been  used  to 
measure  the  velocity  of  currents  of  air  in  mines,  in  France, 
would  yield  valuable  results,  and  the  present  paper  is 
intended  to  record  the  experiments  made  and  the  results 
found  with  two  sizes  of  water  meter  of  that  description. 
Bourdon's  anemometer  is  founded  upon  the  property  of 
a  Venturi  tube  to  exercise  a  sucking  action  through  holes 
bored  into  its  narrowest  section.  Then  by  measuring  the 
intensity  of  this  aspiration  by  means  of  any  form  of 
vacuum  gauge,  and  establishing  the  relation  between  such 
"  vacuum  pressure  "  and  the  velocity  of  the  air  through 
the  tube,  the  instrument  becomes  an  anemometer. 

This  described  property  of  the  Venturi  tube  was 
known  to  Venturi,  and  may  be  found  detailed  at  length  in 
the  account  of  his  experiments  made  in  Modena  about 
1791.  His  own  account  of  these  experiments  was  pub- 
lished in  Paris  in  1797,  under  the  title  "  Recherches 
Experimentales  sur  le  Principe  de  la  Communication 
Laterale  du  Mouvement  dans  les  Fluids. "*  But  Venturi 
made  or  suggested  no  use  of  this  property,  and  with  him 
it  was  merely  a  curious  feature  in  the  working  of  his 
apparatus.  *  *  * 


Application  cf 
the  principle  in 

Bourdon 

Anemometer  to 

measuring 

water. 


*  See  Tracts  on  Hydraulics,  by  Thomas  Tredgold,  second  edition,  London,  1836;  or 
Nicholson's  "Journal  of  Natural  Philosophy,"  Vol.  Ill,  London,  1802,  for  English 
translations;  Gilbert's  "  Annalen,"  Vol.  II  and  Vol.  Ill,  contains  a  German  translation. 


CLEMENS    HERSCHEL  S    PAPER. 


Sizes  and 

character  of 

Meters  used  for 

Tests. 


Description  of 

the  i2-inch 

Meter. 


The  experiments  about  to  be  detailed  were  made  with 
two  sizes  of  Venturi  Water  Meters,  of  precisely  similar 
interior  geometric  dimensions;  one  inserted  into  a  tube 
of  about  nine  feet,  the  other  into  a  tube  of  about  one  foot 
in  diameter.  In  each  case  the  other  intended  dimensions 
may  be  found  from  an  examination  of  the  proportional 
dimensions  given  in  Plate  XXXIII. 

The  throat,  or  the  narrowest  section  of  the  whole 
apparatus,  is  a  cylinder  I  high  or  long,  and  3  in  diameter. 
At  the  distance  of  I  either  way  from  the  throat,  are 
attached  the  frustrums  of  two  cones,  but  the  angles  at 
which  the  cones  would  meet  the  cylinder  are  rounded  off; 
in  case  of  "the  up-stream  cone,  on  a  radius  of  10.38; 
in  case  of  the  down-stream  and  longer  cone  (the  Venturi 
mouth-piece),  on  a  radius  of  45.83.  These  figures  are 
got  from  making  the  tangents  of  the  rounded  off  portions 
in  each  case=i.;  the  angles  at  the  bases  of  the  short 
and  long  cones  being  79  ^  anc^  $7/4  degrees  respectively. 
The  cones  are  produced  in  each  case  until  their  diameter 
=9. ;  making  the  lengths  from  throat  to  end  of  cone 
17.09  and  69.80,  respectively,  and  the  length  of  the  whole 
apparatus  87.89.  These  are  the  intended  dimensions,  in 
feet,  of  the  larger  apparatus  experimented  with  October 
(5-8),  and  by  dividing  all  these  figures  by  9.,  we  get  the 
intended  dimensions  in  feet,  of  the  smaller  Venturi  Water 
Meter,  which  was  tested  June  (9-15),  1887. 

Confining  ourselves  now  to  a  consideration  of  this 
last  named  smaller  apparatus,  the  meter  itself  is  shown  in 
Plate  XXXIV.  The  throat  of  the  venturi,  as  it  was  named, 
is  made  of  cast-iron,  lined  with  brass,  and  comprises  the 
central  cylindrical  and  adjacent  two  curved  portions  of 
Plate  XXXIII.  Its  total  length  was  0.563  feet.  The 
brass  lining  was  about  }4  an  inch  thick,  firmly  set  jn  its 
envelope  of  cast-iron  and  the  joint  between  the  two  end 
faces,  cut  out  in  form  of  a  dove-tailed  circular  slot,  which 
was  then  filled  with  Babbitt  metal  to  guard  against  a 
possible  leakage  of  air  through  the  joint. 


CLEMENS    HERSCHEL  S    PAPER. 

Encircling  the  interior  narrowest  section  is  the  air- 
chamber,  which  is  connected  with  the  interior  with  4 
accurately  and  carefully  drilled  holes,  at  right  angles  to 
the  center  line  of  the  venturi,  and  about  ^  inch  in 
diameter  each.  The  interior  of  the  venturi  was  carefully 
polished  with  emery  dust  after  the  holes  were  drilled, 
making  the  edges  of  the  4  holes,  as  finally  left  and  used, 
perfectly  square  and  sharp. 

To  measure  accurately  the  area  of  the  venturi,  I  had 
made  a  brass  cylinder,  which  exactly  fitted  it,  when  both 
were  of  the  same  temperature.  This  cylinder  I  then 
measured,  on  3  diameters,  with  a  vernier  caliper  made  by 
Darling,  Brown  &  Sharpe,  of  Providence,  R.  I. 

The  averages  in  each  case  of  three  such  measure- 
ments, when  the  plug  had  been  standing  all  day  in  the  air 
at  a  temperature  of  about  68  degrees,  after  a  ^-hour's 
immersion  in  ice-water,  and  immediately  after  taking  it 
out  of  water  of  a  temperature  of  160  degrees  Fahr.,  were 
as  follows : 

At    36  degrees  Fahr.   3.978  inches  ~\  with    no   single    measure- 
68        "          "       3-979     "  ment  positive  as  to  the 

160       "          "       3.980     "       )      final  o.ooi  inch. 

From  which  I  computed  the  area,  at  about  60  degrees 
Fahr.,  to  be  0.08634  square  feet,  and  took  this  as  con- 
stant in  all  the  experiments. 

The  air-chamber  is  bored  at  the  top  to  receive  the 
suction  pipe,  to  which  may  be  attached  any  form  of 
vacuum  gauge. 

To  either  end  of  the  central  cast-iron  member,  the 
venturi,  were  attached  two  wooden  cones,  of  the  general 
interior  dimensions  already  stated. 

These  were  made  of  white  pine  staves,  originally,  or  in 
the  rough,  about  2  inches  thick,  hooped  with  stout  cast- 
iron  hoops,  carefully  planed  and  scraped  to  smoothness 
inside,  then  soaked  in  water  before  using.  The  actual 
dimensions  of  the  cones,  measured  after  soaking  in  water, 


CLEMENS   HERSCHEL'S    PAPER. 

and  again  after  the  experiments,  were  as  follows :  giving 
the  average  of  all  the  measurements  taken  ;  the  differences 
between  .the  first  and  second  set  being  in  no  single 
measurement  over  2  or  3  thousandths  of  a  foot,  and 
therefore  insignificant. 

Smaller  cone,  length,  1.677,  diameters,  .372  and  .991  feet. 
Larger  cone,       "         7.366,         "  .334  and  .992     " 

For  purposes  of  the  experiments,  the  Venturi  Water 
Meter  thus  formed  of  the  two  cones  and  the  venturi,  was 
inserted  in  line  of  a  wooden  tube,  made,  and  treated 
before  using,  as  just  described  for  the  case  of  the  two 
cones.  The  up-stream  length  of  tube  had  the  following 
dimensions : 

Length 5-007;    diameter  at  up-stream  end,  .990, 

at  down-stream  end,  .992. 
Down-stream  tube  i 

Length 5-996;        diameter .996,  .998 

One  foot  from  that  end  of  these  tubes  which  was 
joined  to  either  of  the  two  cones,  each  tube  was  bored  to 
receive  a  piece  of  galvanized  iron  pipe,  ^-inch  inside 
diameter.  To  bore  these  holes,  a  plug  of  soft  wood  was 
carefully  fitted  into  the  tube,  under  the  place  where  the 
hole  was  to  be  bored.  Then  by  using  a  center-bit  auger, 
the  hole  could  be  cut  through  without  roughing  up  the 
inside  edges  of  the  hole,  and  this  hole  left  in  proper  shape 
for  serving  as  the  inside  orifice  of  a  piezometer. 

The  iron  pipe  spoken  of  was  screwed  into  this  hole 
from  the  outside,  but  was  not  allowed  to  penetrate  more 
than  about  half  way  into  the  thickness  of  the  wooden 
stave,  .162  feet  thick,  forming  the  tube  at  that  point. 

To  feed  the  water  to  the  up-stream  tube,  without  loss 
of  head  at  entrance,  it  was  furnished  with  a  cycloidal 
mouth-piece,  likewise  made  of  wooden  staves,  carefully 
smoothed  and  soaked  in  water  as  were  the  other  members. 


CLEMENS  HERSCHEL'S  PAPER. 

This  mouth-piece  had  a  diameter  of  i.ooi  at  the 
outlet,  2.50  feet  at  the  inlet  end,  and  was  1.17  feet  long; 
its  cycloidal  generator  would  itself  be  generated  by  a 
point  on  a  circle  of  0.75  feet  diameter. 

The  experiments  were  conducted  in  the  wheel-pit  of  Place  where. 
the  testing  flume  of  the  Holyoke  Water  Power  Company, 
a  ground  plan  of  which  is  shown  in  Plate  XXXV.  This  is 
a  building  used  by  the  company  named  for  testing 
turbines,  both  for  purposes  of  the  water-measurements 
necessary  in  the  conduct  of  its  own  affairs,  and  for  the 
public.  Its  foundation  masonry  is  first  class  and  well 
grouted  rubble,  afterwards  plastered  with  cement,  and 
lined  with  brick  laid  in  cement.  The  wheel-pit  end-wall, 
built  in  this*same  manner,  is  absolutely  water-tight  under 
20  feet  head  of  water,  and  it  is  believed  that  all  the  other 
walls  are  equally  firm  and  water-tight.  The  floor  con- 
sists of  matched  4-inch  hemlock  plank,  spiked  to  timbers 
resting  on  rows  of  piles,  and  having  2.5  foot  bearing, 
center  to  center,  under  the  wheel-pit ;  4-foot  bearing 
under  the  tail-race.  On  this  first  flooring  is  spiked 
another,  of  4-inch  matched  hard  pine  plank  under  the 
wheel-pit ;  of  2-inch  matched  white  pine  under  the  tail- 
race. 

These  statements  will  give  a  fair  idea  of  the  character 
of  the  structure  which  was  used  as  a  measuring  tank  in 
these  experiments.  For  this  purpose  the  brick  walls 
were  again  plastered  over  with  cement  to  give  a  smooth 
surface  to  measure  from.  The  walls  were  then  marked 
and  divided  off  into  rectangles  by  horizontal  lines  i  foot 
apart,  and  by  vertical  lines  2  feet  apart,  and  all  dimensions 
carefully  taken ;  while  the  floor  was  leveled  on,  both 
when  the  pit  and  tail-race  were  empty,  and  when  full  of 
water.  I  will  not  go  into  further  details  relating  to  the 
determination  of  the  volume  contained  in  the  masonry 
tank  between  any  two  water-surfaces ;  nor  into  the  deter- 
mination of  leakages,  well  known  to  be  one  of  the  most 


CLEMENS  HERSCHEL'S  PAPER. 


Description  of 

Plates  of 
experimental 

apparatus 

and  method  of 

conducting 

Tests. 


troublesome  and  laborious  parts  of  the  conduct  of 
hydraulic  investigations.  Suffice  it  to  say,  that  every 
thought  of  refinement  of  measurement  and  of  computation 
was  applied  to  the  determination  of  volumes,  while  the 
accompanying  leakages  were  measured  at  the  beginning 
and  ending  of  every  experiment  by  noting  the  rate  of  rise 
or  fall  of  the  water  surface  in  the  tank.  This  water  surface 
being  generally  below  the  level  of  the  adjacent  lower  level 
canal,  the  resultant  leakage  was  sometimes  in,  sometimes 
out,  and  sometimes  zero. 

It  was  never  over  o.i  I  cubic  foot  per  second. 

The  heights  of  water  in  the  tank  were  measured  by 
two  hook-gauges,  having,  together,  a  range  -of  about  4 
feet  in  height,  and  the  area  of  the  measuring  tank  was 
about  1,150  square  feet. 

The  whole  experimental  apparatus  is  shown,  in  ground 
plan,  in  Plate  XXXV;  in  elevation,  in  Plate  XXXVI.  The 
water  entering  through  the  gate  At  passed  through  several 
temporary  divisions  put  into  the  forebay  B,  to  quiet  it, 
then  was  fed  to  the  tube  and  Venturi  Meter  by  the  cy- 
cloidal  mouth-piece  above  referred  to.  It  was  discharged 
into  the  tank  C,  whence  it  flowed  into  either  the  box 
D,  leading  through  the  waste-pipe  E,  to  a  by-pass  F,  or 
else,  on  swinging  back  the  spout  G,  it  was  discharged  into 
the  measuring  tank  below.  P  and  Pl  are  piezometers, 
the  difference  of  their  readings  indicating  the  head  acting 
on  the  whole  meter ;  or  loss  of  head,  caused  by  it.  S  is 
the  suction  end  of  the  vacuum  tube  F,  in  these  experi- 
ments, dipped  into  a  tub  of  water,  and  the  whole  tube 
being  34.5  feet  long,  was  long  enough  to  measure  a  per- 
fect vacuum,  had  such  a  thing  been  attainable. 

This  last  named  part  of  the  tube  was  of  course  made 
of  glass,  in  5  lengths  and  with  rubber-tube  joints.  Great 
care  was  taken  to  make  all  the  joints  air-tight,  and  by 
means  of  wrapping  them  with  telegrapher's  rubber-tape, 


CLEMENS    HERSCHEL'S    PAPER. 

and  the  use  of  rubber  cement,  this  was,  it  was  believed, 
successfully  accomplished.  * 

A  drip-box  H  caught  the  leakage  of  the  spout  G, 
while  the  water  was  wasting,  and  discharged  this  leakage 
into  the  waste-pipe  E  by  means  of  the  pipe  /.  J  is  a 
waste-valve  leading  to  the  by-pass  F,  which  helped  to 
regulate  the  height  of  water  in  the  forebay  B. 

At  the  moment  of  one  assistant  opening  the  swing- 
spout  G  to  discharge  the  water  into  the  measuring  tank, 
another  assistant  shut  off  the  pipe  /  by  meaus  of  an 
ordinary  pipe  valve  next  to  the  drip-box  H,  and  he 
opened  it  again,  when  the  swing-spout  was  swung  back 
into  contact  with  the  tank  C.  The  contents  of  the  drip- 
box  Hy  which  wasted  into  the  waste-pipe  E  at  the  close 
of  each  experiment,  when  they  should  have  gone  into  the 
measuring  tank,  were  added  to  the  volume  found  in  the 
measuring  tank. 

The  times  when  the  swing-spout  was  opened  and  when 
shut,  were  taken  by  the  writer,  with  a  stop-watch,  reading 
to  y^  seconds. 

The  practice  of  the  first  three  or  four  experiments 
sufficed  to  get  this  time,  as  near  as  he  could  judge,  exactly 
right.  The  swing-spout  was  handled  so  easily,  by  means 
of  the  long  lever  attached,  that  its  motion  was  very  quick 
and  positive.  Inside  of  the  tank  C,  and  in  front  of  the 
tube  discharging  into  it,  was  a  sliding  gate,  by  means  of 
which  the  discharge  of  the  tube,  and  of  the  Venturi  Meter, 
could  be  regulated. 

It  will  be  noted  that  the  discharge  took  place  under 
water ;  or,  as  it  is  generally  expressed,  the  whole  appa- 
ratus was  submerged.  At  a  later  stage  of  the  experiments, 
when  it  became  desirable  to  reduce  the  amount  of  sub- 
mergence more  than  was  permitted  by  the  position  of  the 
swing-spout,  several  experiments  were  made  with  the 
discharge  escaping  from  tank  C,  through  a  series  of 
holes  bored  into  it;  this  discharge  being  measured,  by 


comparison  with  other  discharges  of  the  whole  system 
of  tube,  Venturi  Meter  and  tube,  when  acting  under  the 
same  total  heads. 

This  series  consists  of  experiments  (70-76). 

Another  odd  set  of  experiments  is  the  series  (56-60). 
To  thoroughly  explain  this  set  it  may  be  best  to  speak 
now  of  the  actual  operations  of  the  Venturi  Meter  as 
applied  to  a  water-pipe  in  ordinary  service. 

If  we  suppose  the  water  in  the  pipe  to  be  still,  the 
height  of  water  in  a  piezometer  placed  just  up-stream 
from  the  meter,  and  in  the  one  formed  by  the  suction 
pipe  which  leads  out  of  the  Venturi  air-chamber,  will  be 
on  the  same  level.  When  the  water  begins  to  flow 
•through  the  Venturi  it  will  cause  the  piezometric  column 
leading  out  of  the  Venturi  to  fall  below  the  straight  line, 
joining  the  surfaces  of  the  water  in  the  two  piezometric 
tubes  placed,  the  one  just  up-stream,  and  the  other  just 
down-stream  from  the  Venturi  Meter ;  this  straight  line 
being  the  best  obtainable  reference  line  at  the  time  the 
experiments  were  being  conducted. 

This  increment  of  fall  I  have  called  the  "  depression  " 
at  the  Venturi.  And  in  the  series  (56-60)  this  depression 
was  seen  through  a  galvanized  iron  pipe  by  "  the  eye  of 
faith  "  alone.  Its  value  was  taken  from  the  values  found 
for  such  depression  in  other  experiments,  when  the  water 
was  passing  through  the  Venturi  with  similar  velocities, 
and  the  degree  of  submergence  was  such  that  the  depres- 
sion could  be  measured  in  form  of  a  vacuum  and  by  the 
vacuum  gauge.  In  the  subsequent  set,  the  October 
experiments,  the  suction  tube  referred  to  was  of  glass,  and 
the  depression  could  be  directly  measured. 

To  resume  a  description  of  the  action  of  the  whole 
apparatus :  As  the  depression  increases,  there  comes  a 
time  when  the  water  level  in  the  suction  tube  will  fall  to 
the  level  of  the  top  of  the  air-chamber,  then  fall  still 
further,  until  finally  it  touches  or  blends  itself  with  the 


6 >i 


PLATE    XXXIII. 

TRANS.     AM.     SOC.     CIV.    ENG'RS. 
VOL.    XVII        NO.    371. 

HERSCHEL     ON 
VENTURI     METER. 


-c 


I 


I 
I 


I    I 


K-l 


d. 


PLATE  XXXIV. 
TRANS.   AM.    SOC.    CIV, 

ENG'RS. 

VOL.    XVII       NO.    371 
HERSCHEL    ON 
VENTURI    METER 


i    « 

iifss 

m 

- 


CLEMENS  HERSCHEL'S  PAPER. 

surface  of  the  stream  of  water  spouting  through  the 
Venturi.  The  moment  the  tendency  to  a  depression  tends 
to  depress  the  water-column  in  the  suction  tube  still 
further,  a  true  sucking  action  commences.  So  long  as  the 
Venturi  end  of  the  suction  pipe  acts  as  a  piezometer,  it  is 
necessary  that  this  pipe  be  connected  with  the  outer  air 
by  means  of  the  pet-cock  above  spoken  of,  to  have  its 
indications  reliable ;  as  otherwise  the  air  contained  in  the 
pipe  between  the  Venturi  and  the  tub  of  water,  or  mercury, 
at  the  lower  end  of  the  other  leg  of  the  suction  pipe,  may 
become  compressed  or  rarified  by  the  action  of  the  water 
backing  up,  or  of  the  Venturi  exhausting  air,  and  thus 
cause  the  piezometric  readings  to  be  in  error.  As  soon 
as  a  true  sucking  action  commences,  however,  the  pet- 
cock  must  of  course  be  closed.  *  * 

The  complete  records  of  the  experiments  are  too  vol- 
uminous to  be  reproduced  in  print.  Before  giving  the 
results  in  the  tabular,  digested  form,  therefore,  some  of  the 
characteristics  of  the  observations  taken  will  be  described. 

The  upper  head-gauge,  column  5  of  the  table,  was 
liable  to  have  large  bubbles  of  air  rise  up  through  it  when 
the  water  in  the  forebay  fell  too  low,  or  was  too  much 
churned  up  by  its  discharge  through  the  head-gate.  When 
this  occurred,  the  experiments  were,  as  a  rule,  suspended, 
and  the  trouble  was  remedied  by  raising  the  water  level 
in  the  forebay,  or  by  causing  the  water  to  flow  through 
longer  channels  before  reaching  the  cycloidal  mouth- 
piece. The  water  in  the  forebay  could  not  be  kept  in 
sight,  and  during  some  of  the  experiments  with  a  low 
stage  of  water  (70-76)  an  eddy  may  have  formed  above 
and  next  the  mouth-piece,  and  carried  air  into  and  through 
the  meter.  I  regard  it  probable  that  the  divergence  of 
experiments  (70-76)  from  the  mean  was  due  to  this 
cause.  But  during  the  experiments  the  indications  of 
head-gauge  No.  I  as  to  air-bubbles  were  regarded  as  con- 
clusive, with  respect  to  the  presence  of  air,  or  of  as  little 


CLEMENS  HERSCHEL'S  PAPER. 

air  as  was  practically  attainable,  in  the  water  carried  by 
the  Venturi  meter.  When  air-bubbles  were  seen  in  this 
gauge-tube,  the  flow  of  water  to  the  mouth-piece  was 
ameliorated  ;  and  when  none  were  seen,  it  was  supposed 
that  there  was  no  need  for  the  amelioration  referred  to. 
At  first,  readings  were  taken  on  this  and  on  head-gauge 
No.  2,  every  minute;  but  after  the  eleventh  experiment 
they  were  taken  at  least  every  half-minute,  and  sometimes 
as  many  as  four  per  minute,  during  the  duration  of  the 
experiment. 

The  oscillations  of  the  water  column  in  head-guage 
No.  I  were  not  large,  being  in  some  experiments  as  little 
as  0.02  in  the  course  of  the  experiment,  and  seldom,  if 
ever,  touching  o.io  as  their  extreme  range. 

The  down-stream  head-gauge,  column  6  of  the  table, 
was  more  troublesome  as  to  air-bubbles  coming  up  in  it, 
and  in  its  range  of  oscillations.  Air-bubbles  could  proba- 
bly have  been  made  to  pass  by  unnoticed,  by  tapping  the 
piezometer  into  the  bottom  of  the  i-foot  tube;  but  the 
original  way  of  tapping  it  into  the  top  of  the  tube  was 
adhered  to,  for  the  very  purpose  of  being  thereby  able 
to  judge,  somewhat,  of  the  amount  of  air  carried  through 
the  meter.  Low  velocities  caused  least  oscillations,  from 
.05  to  .10;  high  velocities  caused  greater  oscillations  in 
the  piezometric  column,  ranging  as  high  as  0.30,  in  some 
cases  0.3 5,  during  the  duration  of  a  single  experiment,  but 
without  any  effort  being  made  to  register  maxima  and 
minima.  The  amount  of  air  carried  through  the  meter 
was  naturally  greatest  during  the  experiments  with  high 
velocities.  It  was  also  governed,  no  doubt,  to  some 
extent  by  the  degree  of  submergence  of  the  whole  appar- 
atus. It  was  never  allowed  to  be  great  enough  to  cast 
palpable  discredit  on  the  indications  of  the  gauge  No.  2, 
having  regard  to  such  indications  consisting  of  thelaver- 
age  of  the  many  readings  (sometimes  forty  or  more)  noted 
down  during  the  course  of  a  single  experiment. 


CLEMENS  HERSCHEL'S  PAPER. 

The  vacuum  gauge,  column  9  of  the  table,  was  sup- 
plied with  water  of  very  nearly  the  same  temperature  as 
that  of  the  water  passing  the  meter.  The  gauge  alongside 
of  the  water-barometer  tube  was  movable,  and  had  for  its 
zero  the  point  of  a  hook-gauge  dipping  into  the  tub  of 
water  that  supplied  the  water  for  the  barometric  column. 
The  point  of  this  hook-gauge,  or  zero  of  the  gauge,  could 
thus  be  constantly  kept  at  the  level  of  the  water  in  the  tub. 

During  extremes  of  velocity,  the  oscillations  of  the 
water  column  were  least;  for  velocities  of  15.  to  35.  feet 
per  second  through  the  Venturi  they  were  greater.  Two 
methods  of  reading  this  gauge  were  used.  In  the  one, 
the  observer  made  his  record  once  a  minute,  mentally 
noting,  before  writing  down  the  observation,  what  was  the 
average  of  the  oscillations  seen.  This  method  gave  an 
extreme  range  of  .10  or  .11  during  the  course  of  any 
single  experiment.  In  the  other  method,  the  observer 
noted  down  heights  seen,  as  fast  as  he  could  write,  so  as 
to  catch  the  very  extremes  of  all  the  oscillations.  This 
method,  gave  sometimes  as  much  as  two  feet  of  oscilla- 
tion during  the  course  of  a  single  experiment.  The_use 
of  a  mercury  column  instead  of  a  water  column  would 
naturally  have  limited  these  ranges  of  oscillation  to  about 
Y1^  of  their  value  as  found.  But  it  was  deemed  best  to 
use  the  water  column  for  purposes  of  an  accurate  repre- 
sentation of  the  forces  at  work  in  the  apparatus.  On  the 
other  hand,  the  air-chamber  was  intended  to  average  or 
to  quiet  the  action  of  these  forces,  as  they  might  act 
through  a  single  orifice  bored  into  the  venturi,  and 
directly  connected  with  a  piezometric  tube  or  with  the 
suction  pipe  of  a  vacuum  barometer.  At  date  of  this 
writing,  I  regard  the  use  of  some  form  of  air-chamber  as 
essential  to  the  good  working  of  a  Venturi  Meter. 

When  the  vacuum  column  was  broken  by  opening  either 
of  the  pet-cocks  which  were  above  the  water  level  in  the 
air-chamber,  the  water  column,  previously  supported  by 


CLEMENS  HERSCHEL'S  PAPER. 

the  existence  of  the  partial  vacuum,  would  drop  instantly, 
then  perhaps  oscillate,  with  a  downward  tendency  in  the 
oscillations. 

Its  fall  could,  as  a  rule,  be  as  instantly  arrested,  by 
closing  the  pet-cock  orifice  with  the  finger ;  and  some- 
times a  number  of  taps  with  the  finger  would  be  telegraph- 
ically repeated  by  apparently  synchronous  movements  of 
the  water  column. 

Before  presenting  the  tabular  results  of  the  experi- 
ments, I  also  present  some  remarks  as  to  the  methods  of 
computation  which  yielded  these  results.  The  first  six 
columns  of  the  table  contain  data,  and  with  what  has  been 
said  above,  will  need  no  further  explanation. 

Column  7  is  a  mere  subtraction  of  Column  6  from 
Column  5. 

Column  8  will  be  as  readily  understood. 

Column  9  contains  data,  being  the  length  of  the  water 
column  held  up  in  the  vacuum  gauge,  and  measured  as 
already  described. 

Column  10  shows  the  working  of  the  3  pet-cocks  that 
were  tapped  into  the  air-chamber,  one  on  top,  one  on  line 
with  a  horizontal  diameter,  and  one  directly  at  the  lowest 
point  of  the  air-chamber. 

Column  1 1  is  the  "  head  on  the  venturi,"  or  Hv,  being 
the  difference  of  level  between  the  water  at,  and  above 
the  venturi,  as  indicated  by  the  head-gauge  No.  I  and  by 
the  vacuum  gauge.  The  elevation  of  the  top  of  the  inside 
of  the  venturi  was  84.704,  and  all  measured  vacuum 
heights  must  be  subtracted  from  this  quantity  to  get  the 
constructive  elevation  of  the  water,  or  locus  of  the  hy- 
draulic gradient,  at  the  venturi.  The  difference  between 
this  locus,  or  elevation  of  the  hydraulic  gradient,  at  head- 
gauge  No.  I  and  at  the  venturi  is  the  "  head  on  *the 
venturi,"  in  the  computations  as  made  and  recorded  in  the 
table. 


CLEMENS    HERSCHEL'S    PAPER. 

Column  12  contains  the  co-efficient  belonging  to  the 
ordinary  computation  of  discharge  through  an  orifice, 
when  the  discharge  is  as  found  during  the  experiment, 
the  orifice  is  the  venturi,  and  the  head  is  Hv. 

Column  13  is  the  locus  of  a  point  at  the  venturi  in  a 
straight  line,  connecting  the  points  in  the  hydraulic 
gradient  found  at  head-gauges  Nos.  I  and  2. 

Column  14  is  the  difference  between  Column  13  and 
84.704,  plus  the  measured  vacuum  heights.  It  indicates 
how  much  the  hydraulic  gradient  was  depressed  at  the 
venturi  below  the  point  given  in  Column  13.  From 
Columns  13,  14  and  5  was  found  the  Hv  to  be  used  in 
experiments  (56-60).  With  a  more  perfect  experimental 
apparatus,  this  and  other  roundabout  methods  of  interpo- 
lation used  in  computing  the  tabular  results  could,  of 
course,  have  been  avoided.  But  with  the  data  at  hand,  it 
was  deemed  better  to  utilize  all  there  were,  in  the  best 
way  possible  rather  than  reject  any. 

Column  1 5  indicates  the  characters  used  in  plotting 
the  experiments. 

Column  1 6  is  Hv  plus  the  height  due  the  velocity  of 
approach  in  the  one-foot  tube ;  and  is  called  Hv. 

Column  17  is  the  co-efficient  corresponding  to  Hv 
when  used  similarly  to  Hv  of  Column  1 1. 

A  star  affixed  to  a  number  in  the  table  indicates  some 
form  of  interpolation. 

Experiment  No.  66  is  worthless  on  account  of  inability 
to  keep  the  head  steady  in  the  forebay.  Experiments  14 
and  15  are  unreliable  on  account  of  too  much  air  in  the 
down-stream  head-gauge  and  passing  the  meter.  And 
I  hold  experiments  70-76  to  be  unreliable,  as  already 
stated. 

It  is  much  to  be  desired  that  the  whole  series  be 
repeated  with  the  more  perfect  means  for  observation, 
which  the  experience  of  this,  the  first  series,  suggested. 


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CLEMENS    HERSCHEL'S    PAPER. 

The  October  set  of  experiments  were  made  with  a 
Venturi  Meter  built  up  inside  of  the  9-foot  trunk  that 
feeds  the  testing  flume.  This  trunk  is  of  the  sort  usually 
built  in  Holyoke,  of  boiler  iron,  to  serve  as  a  penstock  of 
mills. 

Every  alternate  ring,  or  section  of  about  4^-  feet  in 
length,  is  a  spigot-piece,  at  both  ends,  and  the  others  are 
bell-pieces.  Each  ring  is  formed  of  three  plates,  lapped 
and  riveted,  the  bell  and  spigot-joints  also  being  riveted. 
Nominally  9  feet  in  diameter,  very  careful  measurement 
on  15  diameters,  at  the  35  narrowest  sections  of  a  length 
of  about  150  feet,  gave  the  average  area,  rivet-heads  sub- 
tracted, 57.823  square  feet.  The  area  of  the  "  average 
shape"  was  57.742  square  feet. 

This  "  average  shape  "  was  very  nearly  a  true  ellipse, 
having  8.70  and  8.93  for  its  minor  and  major  axes,  the 
minor  axis  being,  the  vertical  one. 

Commencing  at  the  upper  level  canal,  comes  the  usual 
rack  to  keep  out  floating  substances ;  then  a  head-gate,  in 
these  experiments  wide  open,  and  of  no  influence ;  then  a 
piece  of  trunk,  about  7  feet  in  diameter  and  22  feet  long; 
then  a  conical  piece,  8  feet  long,  to  expand  from  the 
7-foot  to  the  9-foot  trunk;  then  the  9-foot  trunk,  in  a 
straight  line  with  the  two  pieces  already  named,  224  feet, 
then  curving  on  a  quarter  circle  of  40  feet  radius  of  center 
line,  and  a  straight  length  9  feet  long,  to  the  vestibule  of 
the  testing  flume,  as  indicated  in  Plate  XXXV. 

Head-gauge  No.  i  was  situated  73.92  feet  down-stream 
from  the  inside  of  the  rack,  the  inside  of  the  rack  being 
35.5  feet  up-stream  from  the  up-stream  end  of  the  9-foot 
trunk.  From  head-gauge  No.  I  to  the  beginning  of  the 
up-stream  cone  was  36.81  feet;  thence  to  center  of  the 
venturi,  16.10  feet;  thence  to  end  of  lower  cone,  69.58 
feet;  thence  to  head-gauge  No.  2,  30.39  feet. 

This  trunk  has  an  inclination  down-stream  of  1.577  m 
IOO  feet,  as  measured  from  the  interior  surfaces  of  the 


CLEMENS    HERSCHEL'S    PAPER. 

orifices  leading  to  head-gauges  Nos.  I  and  2.  All  the 
structures  placed  in  it,  hereafter  to  be  described,  were  set 
in  planes  at  right  angles  to  the  center  line,  or  so  as  to 
have  the  center  line  for  their  geometric  axis.  The  inside 
of  the  top  of  the  venturi  was  on  grade  90.909.  The 
water-level  in  the  upper  canal  at  this  point  is  about  99.90 ; 
that  of  the  lower-level  canal  about  79.90. 

As  above  stated,  the  general  dimensions  of  the  meter 
were  intended  as  given  in  Plate  XXXIII.  The  venturi  is 
shown  in  Plate  XXXVII,  and  was  made,  as  in  the  i-foot 
meter,  of  cast-iron,  lined  with  brass;  differing  from  the 
I-foot  venturi,  however,  in  having  eight  separate  air- 
chambers,  one  for  each  J-inch  hole  leading  out  of  the 
venturi. 

These  several  air-chambers  had  each  a  suction-pipe 
attached,  and  a  pet-cock,  as  shown  in  Plate  XXXVII. 
The  several  suction-pipes  had  each  a  stop-valve,  and 
were  then  assembled  into  the  main  suction-pipe,  which 
led  to  the  vacuum-gauge  or  water-barometer.  By  means 
of  this  arrangement,  any  one,  all,  or  a  combination  of 
several  air-chambers  could  be  connected  with  the  vacuum 
gauge  to  the  exclusion  of  the  others. 

Plate  XXXVIII  shows  the  whole  meter  in  longitudinal 
section.  The  iron  and  brass  venturi  was,  in  this  case,  as 
will  be  seen,  a  true  cylinder,  about  3  feet  in  diameter  and 
only  i  foot  long.  Its  area  was  7.07425  square  feet,  as 
determined  from  a  measurement,  with  a  vernier  slide-rod, 
on  1 2  diameters ;  4  at  each  end  and  at  the  center  of  the 
cylinder. 

At  either  end  of  the  venturi  was  a  wooden  connecting- 
piece,  made  to  flare  outwardly  in  the  curves  shown  in 
Plate  XXXIII,  and  built  up  of  staves,  hooped  with  strong 
cast-iron  frames,  turned  and  smoothed  in  a  lathe  and 
soaked  in  water  before  setting.  At  either  end  of  the  cen- 
tral portion  thus  formed  came  the  two  cones,  consisting 
of  planed  pine  strips  nailed  to  circular  frames  or  hoops, 


CLEMENS    HERSCHEL'S    PAPER. 

set  inside  the  9-foot  trunk.  This  construction  of  the 
cones  did  not  leave  them  so  smooth,  at  all  the  joints  and 
butts,  as  was  the  case  with  the  I -foot  cones,  of  course; 
the  whole  surface  was,  however,  much  smoother  than  the 
interior  of  the  iron  trunk  at  either  end.  Two  water-tight 
bulk-heads  set  in  the  trunk  at  either  end  of  the  central 
portion  above  referred  to,  and  a  man-hole  cut  into  the 
trunk  from  the  outside  between  these  bulk-heads,  gave 
access  to  the  outside  of  the  venturi  during  the  experi- 
ments. 

In  these  experiments  the  head-gauges  were  hook- 
gauges,  measuring  water-levels  inside  of  stout  boxes,  that 
were  connected  with  the  9-foot  trunk  by  |-inch  pipes. 
These  f-inch  pipes  were  connected  with  short  brass 
ajutages  let  into  the  shell  of  the  trunk,  and  smoothly  filed 
off  on  the  inside.  The  trunk  itself  was  tapped  to  receive 
these  ajutages,  in  the  case  of  each  gauge,  at  the  top  of 
one  of  the  smaller  or  spigot  rings,  about  I  foot  up-stream 
from  its  entrance  into  one  of  the  larger  or  bell  rings. 

The  quantity  passing  the  meter  was  measured  over 
the  weir  of  the  testing  flume.  This  is  a  permanent  weir, 
having  a  wrought-iron  sharp  edge,  which  can  be  used 
without  end-contractions  on  a  length  of  about  20  feet,  or 
with  end-contractions  on  shorter  lengths. 

It  was  used  with  end-contractions  on  a  6-foot  length 
in  experiments  (1-7),  and  without  end-contractions  in  the 
remaining  experiments.  About  10  feet  up-stream  from 
the  weir  is  a  horizontal  perforated  brass  tube  set  some  9 
inches  above  the  floor  (which  in  turn  is  5.9  feet  below  the 
crest  of  the  weir),  this  tube  being  connected  with  a  gal- 
vanized iron  bucket  set  in  a  recess  in  the  wall  and  fitted 
with  a  hook-gauge  for  measuring  depths  upon  the  weir. 
I  have  always  used  a  light  leveling-rod,  |-inch  square, 
graduated  on  all  four  sides,  by  Darling,  Brown  &  Sharpe, 
of  Providence,  R.  I.,  brass-tipped  at  the  ends  and  set 
directly  on  the  hook,  to  compare  weir  heights  with  the 


PLATE   XXXVII. 

TRANS.     AM.     8OC.     CIV.     ENG'RS. 
VOL.    XVII      NO.   371. 

HER8CHEL    ON 
VENTURI     METER. 


Experts?  u>?tt#. 


CLEMENS  HERSCHEL'S  PAPER. 

setting  of  the  hook-gauge.  Two  racks  deaden  the  water 
before  it  reaches  the  line  of  brass  tube  that  leads  to  the 
hook-gauge  bucket. 

As  some  of  the  weir  heights  exceed  the  limit  of  the 
Francis  experiments,  I  used  in  the  computations  of  these 
quantities  the  co-efficients  given  in  Hamilton  Smith's 
"  Hydraulics." 

These  are  the  result  of  a  careful  sifting  and  digest  of  all 
attainable  original  publications  of  the  records  of  reliable 
experiments  on  the  discharge  over  weirs,  inclusive  of 
those  made  by  James  B.  Francis,  and  recorded  in  ''Lowell 
Hydraulic  Experiments."  Their  results,  differ  from  the 
results  of  the  Francis  formula  in  the  present  instance  as 
follows,  giving  a  few  characteristic  differences. 


Difference  to  Reduce  F.  Quantity  to  S.  Quantity. 

Tl       +V»           «-f»      '\V    " 

6-foot  Weir. 

2o-foot  Weir. 

Per  cent. 

Per  cent. 

0.2 

-  1-7 

+  2.0 

0.8 

-     .O 

—  0.7 

I.O 

-     .1 

—  0.45 

2.0 

-  I.O 

+  i.o 

2-5 

+  14 

+  i-5 

The  measurement  of  leakages  was  conducted  with  the 
same  care  that  obtained  in  the  June  experiments  already 
spoken  of.  They  could  in  all  cases  be  measured  by  the 
variations  in  the  water-level  of  a  defined  area,  the  proper 
allowance  being  then  made  for  an  increased  or  a  dimin- 
ished head  upon  the  orifices  causing  leakage  for  the 
duration  of  each  experiment ;  in  one  case,  that  of  the  two 
bulk-heads  either  side  of  the  venturi,  the  leakage,  an 
insignificant  quantity,  was  pumped  out  and  measured  in 
pails.  The  total  leakage  never  exceeded  0.72  cubic  feet 
per  second,  and  ranged  from  that  down  to  0.47,  or  from 


CLEMENS  HERSCHEL'S  PAPER. 

about  0.3  to  4  per  cent,  respectively,  of  the  quantity  pass- 
ing the  meter. 

In  these  experiments,  also,  the  discharge  of  the  meter 
was  a  submerged  one.  The  water  at  the  extreme  down- 
stream end  of  the  9-foot  trunk  always  stood  higher  than 
the  top  of  the  trunk. 

Before  setting  the  Venturi  meter  into  the  9-foot  trunk, 
but  after  the  head-gauges  subsequently  used  in  the  Venturi 
meter  experiments  had  been  established,  a  series  of  experi- 
ments were  made  to  test  the  loss  of  head  in  the  original 
9-foot  trunk.  The  results  of  this  series  are  given  in  the 
table  which  follows. 

The  area  was  taken  =  57.823  square  feet  as  above 
stated. 

D  =  8.58,  though  the  "  average  shape  "  was  an  ellipse 
and  not  a  circle.  f 

/=  152.88,  being  the  distance  between  centres  of 
piezometric  brass  ajutages  above  spoken  of. 

Each  experiment  is  based  upon  the  average  result  of 
not  less  than  forty  consecutive  half-minute  readings. 

In  this  and  the  following  series  of  experiments,  taking 
their  supply  of  water  from  the  upper  level  canal  at 
Holyoke,  an  extra  gate  tender  was  stationed  on  duty  to 
keep  the  upper  level  steady.  By  constantly  wasting  out 
of  the  upper  level,  at  a  point  some  distance  from  the 
head-gates,  then  keeping  the  water  steady  at  this  point 
by  regulating  the  amount  wasted,  and  with  the  aid  of  a 
canal  a  mile  long  and  averaging  125  feet  wide,  as  was  the 
case,  this  was  reasonably  well  accomplished.  During  the 
course  of  a  single  experiment  the  canal  seldom  varied  as 
much  as  o.io  in  level.  Then,  in  the  well-known  formula 

v=n^r  s,  s  being  equal  to—  (see  Hamilton  Smith's  "Hy- 
draulics," p.  271,) 

vt  h  and  ;/  have  the  following  corresponding  values. 


CLEMENS    HERSCHEL'S    PAPER. 


V 

A 

n 

Feet  per  second. 

Feet. 

Co-efficient. 

°-5 

O.OOI2 

I2I.9 

I.O 

.0049 

I2O.6 

l-S 

.0128 

III.Q 

2.0 

.0238 

109.4 

2-5 

•0375 

109.0 

3-o 

.0548 

108.2 

3-5 

.0763 

107.0 

4.0 

.1012 

106.2 

4-5 

.1295 

105.6 

The  results  of  the  thirteen  experiments  made,  plotted 
so  regularly,  and  the  points  were  so  close  together,  that 
there  is  hardly  a  choice  in  reliability  between  points  taken 
from  plotted  curves  at  regular  intervals,  as  given  in  the 
table,  and  the  direct  results  of  experiment.  I  judge  from 
the  disagreement  of  the  results  above  given,  with  those 
found  at  other  places,  but  on  longer  tubes,  either  that 
piezometers  do  not  correctly  indicate  the  h  of  the  formula 
(see  Hamilton  Smith's  "  Hydraulics,")  or  else  that  a 
uniform  and  non-accelerative  regime  of  the  flow  of  water 
through  the  trunk  had  not  become  established  in  the 
comparatively  short  length  at  command  for  purposes  of 
measurement.  This  latter  circumstance  would,  in  most 
cases,  prevent  any  attempt  to  compute  the  flow  of  water 
through  mill  trunks,  and  in  many  cases  of  city  water 
pipes,  by  the  use  of  the  formula  v=n\Jrs,  or  of  any  other 
formula  for  the  discharge  of  pipes ;  whose  general  co- 
efficients can  only  be  established  for  the  case  of  a  perfectly 
uniform,  permanent  flow;  three  modifying  conditions,, 
namely,  those  of  perfection,  uniformity,  and  permanency, 
which  are  very  difficult  to  obtain  in  practice. 

Passing  now  to  the  description  of  the  table  about  to- 
be  given : 


CLEMENS  HERSCHEL'S  PAPER. 

Explanation  of  Columns  I  to  8  will  hardly  need  explanation  other 

than  that  already  above  written.  All  the  data  tabulated 
are  the  averages  of  consecutive  half-minute  readings, 
except  in  case  of  the  head  on  the  weir,  where  the  usual 
one-minute  interval  between  readings  was  adhered  to. 

Columns  9  and  10  will  be  clear,  when  it  is  remembered 
what  was  above  said  with  regard  to  depression  of  the 
piezometric  water  column  in  the  branch  of  the  suction- 
'  pipe  which  leads  directly  out  of  the  air-chamber,  and 
concerning  the  vacuum-gauge  formed  by  the  other, 
descending  leg  of  the  same  suction-pipe ;  remembering, 
moreover,  that  the  plane  of  division  between  the  action  of 
these  two  forms  of  the  venturi  gauge  lies  on  grade  90.909, 
as  above  stated. 

Column  1 1  brings  us  to  a  peculiarity  in  this  method 
of  metering  water,  first  revealed  by  this  series  of  experi- 
ments, viz.,  that  the  indications  of  the  venturi  depression, 
or  vacuum  gauge,  are  different,  according  as  the  venturi 
has  been  pierced  upon  a  different  diameter.  *  * 

As  these  experiments  were  made  for  the  sole  purpose 
either  of  discovering  or  of  perfecting  a  new  and  practical 
method  of  gauging  water,  I  have  not  pursued  the  study 
of  this  apparent  idiosyncrasy  of  the  meter  any  further  than 
as  stated  in  the  Table.  As  I  translate  the  results,  they 
mean  that  the  venturi  must,  in  all  cases,  be  pierced 
for  connection  with  the  air-chamber  vertically  at  its 
crown,  and  may  be  pierced  radially  at  as  many  additional 
points  as  we  please,  without  affecting  the  reading  of  the 
standard  crown  orifice.  T  have  no  experimental  results  to 
guide  me  in  a  choice  between  several  venturi  orifices  and 
air-chambers  (one  at  the  crown  always  included),  or  only 
a  crown  orifice ;  or  between  air-chambers  separate  and 
distinct  for  each  orifice,  as  in  the  October  experiments, 
and  an  air-chamber  common  to  several  orifices  and 
encircling  the  venturi,  as  in  the  June  experiments.  Still, 
as  my  feeling  on  the  subject,  being  that  of  a  person  who 


CLEMENS    HERSCHEL'S    PAPER. 

has  worked  with  the  two  forms  of  meter,  may  be  interest- 
ing, I  will  state  that,  at  present,  I  should  favor  the  general 
form  of  air-chamber  and  of  orifices  used  in  the  June 
experiments. 

Column  12  will  need  no  explanation.  In  this  set  of 
experiments,  with  the  glass  suction-pipe  next  the  venturi 
and  the  separate  air-chambers,  these  pet-cocks  were  of 
subordinate  value.  To  open  a  pet-cock,  so  long  as  the 
depression-gauge  (not  vacuum-gauge)  is  acting,  does  not 
disturb  the  piezometric  water  column. 

Columns  13  to  16  demand  no  further  explanation  than 
was  given  for  the  similar  columns  in  the  table  relating  to 
the  June  experiments. 

As  regards  the  range  or  oscillations  of  the  several 
gauges,  in  the  space  of  one  experiment,  during  this  series, 
it  was : 


In  head-gauge  No.  I,  seldom  so  much  as °-°5  feet. 

«         «        "2,          "  "        0.05     " 

In  the  depression-gauge,     "  "        o.i  I     " 

In  the  vacuum-gauge,          "  "        0.30  to  0.50     " 


as  a  result  of  ^-minute  readings,  and  with  no  attempt  to 
record  absolute  maxima  and  minima. 

The  quantity  of  water  discharged  must  have  been  very 
nearly  uniform  in  its  flow  per  second. 

I  pass  now  to  a  brief  discussion  of  the  results  as  found     Consideration 

T<    i   i         TVT  i  of  Results 

in  Tables  No.  I  and  2.  shown  by 

As  a  measure  of  comparison  of  the  uniformity  of  the  Tables, 
results  found  with  the  two  Venturi  Meters  experimented 
on  in  June  and  October,  1887,  I  suggest  the  range  of 
co-efficients  known  to  exist  in  the  case  of  the  weir,  or  of 
a  simple  orifice.  The  weir  has  hitherto  been  regarded  as 
a  standard  method  of  gauging  water ;  yet  every  one  who 
has  practiced  with  it  knows  how  carefully  all  its  dimen- 
sions must  be  proportioned,  and  the  water  led  to  it,  in 


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IN   ro  -^t-  invo   t-^oo   ON  O   H   pi   ro  -^-  i 
CN  CM  N  Pi  0  pi  pi  Pi  roromroro 


CLEMENS    HERSCHEL'S    PAPER. 

order  that  it  may  give  truthful  or  accurate  results.  The 
range  of  the  co-efficients  entering  into  any  proposed 
formula  for  the  discharge  over  a  weir,  can  be  and  has 
been  limited  by  limiting  the  general  and  proportional 
dimensions  of  the  apparatus  and  water  depths  to  which 
the  formula  was  to  be  applicable.  And  the  most  positive 
results  are  undoubtedly  found  by  taking  such  a  limited 
formula,  constructing  the  weir  or  other  apparatus  in 
accordance  with  the  dictates  of  the  experiments  on  which 
it  was  founded,  and  then,  practically,  by  repeating  the 
experiments,  repeating  the  attainment  of  the  original 
results.  And  wherever  this  can  be  done  with  a  weir,  the 
method  of  experiments  made  at  Lowell  by  James  B. 
Francis,  and  the  formula  based  upon  them  will,  no  doubt, 
long  remain  the  standard  method  and  formula  for  weir 
measurements.  But  without  such  close  limitation  and 
imitation,  or  taking  depths  upon  the  weir  ranging  only 
from  0.3  to  2.0  feet,  and  taking  weirs  both  with  and 
without  end-contractions,  the  co-efficient  varies  from  .660 
to  .580  (see  Plate  VII,  Hamilton  Smith's  "  Hydraulics,") 
or  12  per  cent. 

Taking  only  weirs  without  end-contractions,  the  range 
is  from  .660  to  .614,  or  about  7  per  cent.  In  case  of  the 
I  foot  Venturi  Meter,  and  velocities  through  the  venturi, 
ranging  from  5  to  50  feet  per  second,  this  range  of 
co-efficient  was  6.5  per  cent. ;  in  case  of  the  Q-foot 
Venturi  Meter,  and  velocities  through  the  venturi,  ranging 
from  5  to  36  feet  per  second,  it  was  3.3  per  cent.  But 
better  than  this  is  the  fact  that  the  two  meters,  though 
differing  so  much  in  their  size  and  structure,  showed  a 
total  combined  range  of  co-efficient  no  greater  than  the 
smaller  one  alone,  or  only  6.5  per  cent.;  taking  the 
co-efficients  based  on  Hv,  being  those  corrected  for 
velocity  of  approach,  and  using  that  simplest  of  "all 
hydraulic  formula,  v=^  2g  Hv. 


CLEMENS    HERSCHEL'S    PAPER. 

Though  the  areas  of  discharge  were  as  81  to  I,  and 
the  interior  fractional  surfaces  were  widely  different,  the 
resultant  co-efficients  are  at  extreme  points  only  6.5  per 
cent,  apart ;  and  the  deviation  of  any  single  experiment 
from  the  resultant  mean  is  3.0  per  cent,  in  case  of  the 
i -foot  tube,  excluding  the  unreliable  interpolated  results, 
and  only  y2  per  cent,  in  case  of  the  Q-foot  trunk  for  its 
whole  range  of  velocities.*  If  we  compare  this  to  the 
case  of  a  discharge  through  various  orifices,  the  result  is 
still  more  gratifying.  To  the  wearied  sojourner  among 
such  tables  of  discharge  —  ranging  in  their  co-efficients 
from  the  familiar  0.6  or  |,  up  to  the  mystical  co-efficients 
in  the  eighty's  and  ninety's,  said  to  have  been  found  by 
some  one  "  on  large  sluice-gates  in  France"  (and  occa- 
sionally met  with  in  the  current  practice  of  the  hydraulic 
engineer) — a  consistency  in  co-efficients  as  above  found 
for  the  hydraulic  apparatus  herein  described,  is  indeed 
refreshing.  We  appear  to  have  here,  at  last,  an  apparatus 
for  gauging  liquids  which  may  range  in  its  dimensions,  its 
materials  of  construction  and  in  manner  of  use,  so  as  to 
cover  all  ordinary  practice,  and  yet  have  only  6.5  per 
cent,  of  range  of  co-efficient,  at  the  same  time  requiring 
only  the  simplest  of  observations  and  of  formulas  to  work 
with.  Or  by  limiting  the  use  of  the  meter  to  velocities 
greater  than  9  feet  per  second  through  the  venturi,  being 
about  i  foot  per  second  through  the  pipe  thereto  appurte- 
nant, all  the  ranges  of  variations  above  given  become 
materially  less. 

I  said  above  that  we  "  appear"  to  have  such  an 
apparatus,  or,  to  completely  express  the  underlying 
thought,  we  appear  to  have  it  in  the  light  of  the  only  two 
sets  of  experiments  yet  made,  so  far  as  I  know,  with  a 
Venturi  Meter  set  in  line  of  a  pipe.  But  further  experi- 
ment will  be  needed  to  confirm  or  upset  such  a  conclusion, 

*  See  Plate  XXXIX,  showing  plotted  results. 


HEAD  ON  THE  VENTURI  =HVJN  FEET. 
c/i  5  c/1  o 


rirU 


Sfc 


\,N 


^ 


A 


PLAT 
S.AM.S 
L.XVll 


TE  XXX  IX 
.SOC.CIV.ENGRS. 
ll  NO.37J. 
HCRSCHELON 
VENTURI  METER. 


o—      ruoj^oj^Noocoo  i\> 

TOTAL  HEAD  ON  THE  METER- H,  IN  FEET 


CLEMENS  HERSCHEL'S  PAPER. 

and  one  object  of  the  present  paper  is  to  invite  such 
further  experiments.* 

The  reason,  I  will  suggest,  why  the  co-efficients  be- 
longing to  this  form  of  gauging  apparatus  are  so  nearly 
uniform,  is  largely  on  account  of  the  close  similarity 
between  the  conditions  assumed  by  theory  and  those 
found  in  actual  practice,  regarding  now  the  state  of  the 
liquid  as  it  passes  through  the  venturi.  Here,  if  any- 
where, water  may  be  supposed  to  flow  as  though  com- 
posed of  the  traditional  "  filaments"  of  the  school-books; 
while  the  bubblings  of  a  boiling,  seething  caldron  are  but 
little  more  violent  and  irregular  than  the  motions  of  the 
alleged  "  threads "  of  water,  as  we  find  that  water  in 
ordinary  practice,  and  as  it  flows  in  canals  or  even  in  the 
ordinary  line  of  pipes,  or  in  tubes. 

Still  the  co-efficient  is  not  the  same  for  all  velocities ; 
it  is  less  for  higher  velocities  than  it  is  for  lower  ones  in 
the  October  experiments,  while  the  reverse  holds  true  in 
the  June  experiments ;  the  meter  does  not  appear  to  be 
applicable  for  velocities  below  5  feet  per  secondf  through 
the  Venturi,  or  about  J-foot  per  second  through  the  pipe 
in  which  it  is  placed ;  and  the  co-efficient  is  not  equal  to 
one,  except  in  one  instance. 

The  difference  between  the  equation  giving  the  locus 
of  the  co-efficients  as  applicable  to  the  9-foot  trunk  and 
to  the  i -foot  tube,  may  be  due  to  difference  in  asperity  of 
their  interior  surfaces;  some  of  it  may  possibly  be  due  to 
the  shortening  of  the  9-foot  cones,  caused  by  the  trunk 
measuring  only  8.7  feet  high  instead  of  9  feet  as  supposed. 


*  While  this  paper  is  being  written  I  am  in  receipt  of  the  October  number  of  the  Journal 
of  the  Association  of  Engineering  Societies,  which  gives  the  results  of  experiments  upon 
similar  forms  of  discharge,  but  discharging  from  a  tank,  and  through  an  orifice  of  only  about 
0.03  feet  in  diameter,  and  in  which  the  same  co-efficient  is  likewise  found  nearly  equal  to  i. 

t  For  the  case  of  v  =  0  >  Hv  is  also  =  0 ,  and  the  co-efficient  becomes  =  -&  which  may 
be  any  assignable  quantity. 

This  justifies  the  curiously  diverging  form  of  the  curves  of  co-efficients  for  the  two 
Venturi  Meters,  as  shown  on  the  diagram. 


CLEMENS    HERSCHEL'S    PAPER. 

Part  of  the  deficiency  from  the  value  i.  may  be  due  to 
defective  guidance  of  the  water  as  it  approaches  the 
venturi.  It  would  have  been  better,  no  doubt,  to  have 
rounded  off  the  angle  with  which  the  up-stream  end  of 
the  smaller  cone  meets  the  up-stream  pipe  or  trunk ; 
better  still,  to  have  made  that  portion  of  the  meter  up- 
stream from  the  venturi  of  a  form  which  would  be  gener- 
ated by  the  revolution  about  the  central  axis  of  an  ogee 
curve.  In  the  case  of  the  discharge  from  an  open  canal 
or  from  a  tank,  this  portion  of  the  meter  could  be  sup- 
pressed entirely,  and  in  its  stead  be  placed  only  a  mouth- 
piece, having  the  form  of  the  contracted  vein  to  feed  the 
venturi ;  with  a  head-gauge  reading  directly  the  water- 
level  in  the  tank  or  canal. 

It  is  also  an  interesting  question  whether  the  vacuum- 
gauge  is  indicative  of  the  mean  velocity,  or  of  the  veloc- 
ity of  the  exterior  filaments  of  the  body  of  water  passing 
through  the  venturi,  or  of  both,  and  what  is  the  precise 
meaning  of  the  readings  of  this  and  other  piezometers 
tapped  into  pipes  of  flowing  water.  In  our  present  very 
imperfect  knowledge  of  the  action  and  precise  meaning 
of  the  indications  of  such  piezometric  columns,  especially 
when  applied  to  tubes,  but  little  can  be  positively  affirmed 
about  them. 

Loss  of  head  is  still  the  only  difficulty  to  contend 
against  in  the  practical  application  of  the  meter  for  mill 
purposes.  For  purposes  of  metering  a  city,  or  domestic 
water  supply,  or  water  used  for  purposes  other  than 
power  in  mills,  this  loss  is  insignificant.  In  the  other  case 
named,  and  for  a  9-foot  trunk,  it  would  be  about  I  foot, 
when  the  mean  velocity  through  the  trunk  was  2.7  feet, 
and  J-foot  for  a  velocity  of  about  1.9  feet.  If  the  circum- 
stances are  such  that  this  loss  of  head  is  not  permissible, 
or  cannot  be  paid  for  by  the  delivery  of  enough  more 
water  to  yield  to  the  consumer  an  equivalent  amount  of 
power,  then  this  meter  cannot  be  used  in  a  form  that 


CLEMENS    HERSCHEL'S    PAPER. 

would  make  it  continuously  the  sole  outlet  or  inlet  of  the 
water  to  be  metered.  It  could  be  applied  in  those  cases 
•either  at  the  inlet  or  outlet,  in  the  penstock  or  in  the  tail- 
race,  but  would  have  to  be  provided  with  some  form  of 
byepass  to  be  kept  open  at  all  those  times  when  the 
operation  of  metering  the  water  was  not  actually  going 
on.  This  could  be  readily  done  in  the  case  of  an  open 
feeder  or  of  most  any  tail-race,  and  as  the  operation  of 
metering  need  require  so  little  time,  barely  five  or  ten 
minutes,  there  could  hardly  be  any  objection  made  by 
the  consumer  to  this  plan  of  measuring  water.  It  prob- 
ably need  not  be  pointed  out  that  the  whole  apparatus 
could  literally  be  submerged,  or  covered  with  water,  and 
yet  be  conveniently  used  and  act  as  it  ought  to,  so  long 
as  it  afforded  the  only  outlet  from  one  body  of  water  to 
another,  and  that  its  advantages  in  freedom  from  any 
moving  parts,  and  from  liability  to  be  stopped  up  or  put 
out  of  order  by  floating  substance  or  by  ice,  are  very 
great. 

Writing  so  soon,  only  a  few  weeks  after  the  close 
of  the  second  set  of  experiments,  I  do  not  very  likely 
allude  to  all  the  capabilities  of  the  meter,  and  have  hardly 
broached  the  interesting  subject  of  the  theory  of  the  in- 
strument. It  seems  to  me  that  it  may  in  many  instances 
replace  the  use  of  a  weir,  being  easier  applied  and  equally 
or  more  accurate,  and  it  can  be  used  where  a  weir  is  en- 
tirely inapplicable. 


MR.  CLEMENS  HERSCHEL  (in  reply  to  questions  asked  Discussion 
at  the  time  of  reading  the  paper). — In  its  completed  form, 
the  Venturi  Meter  is  an  instrument  to  gauge  the'quantity 
of  water  flowing  in  a  pipe,  by  measurement  of  an  abrupt, 
artificially  produced  depression  in  the  hydraulic  gradient. 
To  explain  more  particularly,  suppose  a  pipe  full  of  water 
the  water  in  a  state  of  rest.  Piezometers  placed  on  such 


CLEMENS    HERSCHEL'S    PAPER. 

a  pipe,  will  have  the  water  stand  in  them  at  points  situated 
all  on  one  level. 

In  Plate  XL,  suppose  PP  to  be  such  a  pipe,  at  one 
time  "  submerged,"  or  under  a  head,  to  the  extent  I  P, 
and  again,  only  to  the  extent  a  P.  Next,  suppose  the 
water  to  take  any  velocity  through  the  pipe  (no  meter 
being  yet  supposed  inserted),  sufficient  to  cause  the  water 
in  the  piezometer  to  stand  on  the  line  22  and  bb,  respec- 
tively, according  as  the  amount  of  submergence  was 
originally  I  P  or  a  P.  This  line  22,  or  bb,  is  what  I  have 
called  the  "  hydraulic  gradient."  Next,  suppose  the 
meter  inserted  in  the  pipe ;  upon  which,  the  water  level 
at  the  up-stream  piezometer  will  remain  at  2,  but  at  the 
piezometer  which  is  set  on  the  venturi,  the  water  level  or 
hydraulic  gradient  will  drop  to  3,  then  rise  again,  at  the 
end  of  the  meter,  up  to  within  a  small  distance  below  its 
former  position  (this  distance  representing  the  "  loss  of 
head  "  due  the  whole  apparatus),  then  will  run  parallel  to 
its  former  position,  as  shown  at  3  on  the  down-stream 
piezometers.  The  experiments  have  shown  that  the 
velocity  of  the  water,  or  the  discharge  through  the  nar- 
rowest section  of  the  meter  through  the  "  venturi,"  is  that 
due  the  head  on  the  venturi  (as  represented  by  the 
difference  in  level  of  two  points  in  the  "  hydraulic 
gradient,"  one  taken  just  above  the  meter  and  the  other 
at  the  venturi),  with  a  co-efficient,  which  is  remarkably 
constant,  whether  applied  to  a  rough  meter  and  for  a 
9-foot  pipe,  or  to  a  smooth  one  for  a  i-foot  pipe,  and  for 
all  velocities  through  the  pipe  ranging  from  ^  to  six  feet 
per  second.  If  this  co-efficient  is  taken  without  further 
measurement  at  98  per  cent.,  we  may  be  certain  from 
experiments  so  far  made  that  we  shall  rarely  be  over 
2  per  cent,  out  of  the  way.  Going  back  a  little,  let  us 
take  now  the  other  case  of  submergence,  originally  repre- 
sented by  the  hydraulic  gradients  aa  and  bb.  It  is  plain 
that  the  water  level  in  the  piezometer  which  is  set  on  the 


I I 


I      i 


I    I 
I    I 


PLATE  XL. 


CLEMENS    HERSCHEL'S    PAPER. 

venturi  cannot  fall  below  the  surface  of  the  stream  spout- 
ing through  the  venturi. 

But  so  much  of  the  "  depression "  in  the  hydraulic 
gradient  at  this  point  due  the  velocity  of  the  water,  which 
lies  below  the  surface  of  the  stream  just  named,  will  be 
indicated  or  exhibited  by  the  sucking  action  or  aspiration 
or  "  vacuum"  spoken  of  in  the  paper;  and  in  measures  of 
a  column  of  water  lifted,  will  exactly  equal  that  portion  of 
the  "  depression,"  as  shown  in  Plate  XL  (or  as  it  may  be 
computed),  which  lies  below  the  surface  of  the  stream 
spouting  through  the  venturi.  In  Plate  XL  it  is  equal  to 
the  distance  v  c,  indicated  by  the  reference  marks. 

This  is  the  case  in  which  some  form  of  vacuum-gauge 
is  necessary  at  the  venturi,  when  separate  gauges  are  used 
at  the  up-stream  piezometer  and  at  the  venturi,  as  was 
done  during  the  experiments  related  in  the  paper.  No 
such  complication  is  necessary,  however,  in  practice. 
As  the  measure  sought  is  the  difference  of  pressure 
immediately  above  the  meter  and  at  the  venturi,  a  single 
pressure-gauge  suffices.  The  logical  possibilities,  depend- 
ing on  the  degree  of  submergence  of,  and  velocity  through 
the  pipe,  are  three,  and  are  exhibited  by  the  table : 


Above  the  Meter. 

At  the  Venturi. 

I 

Pressure. 

Pressure. 

2 

Pressure. 

Vacuum. 

3 

Vacuum. 

Vacuum. 

But  in  any  event  there  will  be  a  "head  on  the  venturi," 
or,  what  is  the  same  thing,  Column  I  minus  Column  2  of 
the  tabular  quantities  will  always  be  positive,  and  will 
indicate  pressure,  and  may  be  measured  by  a  single- 
pressure  gauge. 

Answering  question  which  relate  to  the  temperature 
of  the  water  during  the  experiments  recorded  in  the  paper, 


CLEMENS  HERSCHEL'S  PAPER. 

I  will  state  that  this  varied  from  67  to  71  degrees  Fahr. 
during  the  June  experiments,  with  the  temperature  of  the 
air  in  the  wheel-pit,  and  of  the  water  in  the  tub  of  the 
pressure-gauge,  varying  from  66  to  71  degrees. 

During  the  October  experiments  the  temperature  of 
the  water  was  57-57.5  degrees. 

It  is  undoubtedly  true  that  all  hydraulic  formulas  are 
affected  by  the  temperature  of  the  water,  when  that  tem- 
perature passes  beyond  those  ordinarily  found  in  running- 
water  ;  but  in  ordinary  practice,  and  without  reference  to 
water  artificially  heated,  and  as  it  is  at  times  found  in 
steam  engineering  practice,  no  account  has  ever  been  or 
need  be  taken  of  temperature  that  the  author  knows  of. 

The  formula  used  in  the  computations,  it  will  be 
observed,  supposes  a  discharge  through  an  orifice,  under 
pressures  crudely  represented  by  the  hydraulic  gradient. 

A  more  scientific  way  would  have  been  to  make  use 
of  the  hydraulic  principle  first  enunciated  by  Dubuat,  but 
disputed  by  Navier  and  others,  that  the  pressure  against 
any  point  in  the  walls  of  any  vessel  or  pipe  is  always 
equal  to  that  of  the  contained  fluid,  supposed  to  be  in  a 
state  of  rest,  less  the  height  due  the  velocity  past  that 
point. 

Or,  passing  to  algebraic  symbols,  if 
P  be  the  pressure  in  terms  of  the  height  of  a  column  of  water 

at  the  point  P,  Plate  XL,  and 
Pt    "          "     at  the  point  V  of  Plate  XL;   if 
v      "      velocity"        "       P,  and 
vi    "  "         "       "       V\   also 

Ps   "      pressure  if  the  water  be  supposed  to  be  still;   then 

vz 

n         D 

Pl 


and  VI--=Q  v,  from  the  construction  of  the  meter. 


CLEMENS  HERSCHEL'S  PAPER. 
Subtracting  the  equations,  we  have : 

zg       2£-~8i2£- 

But  P —  Pi  is  what  we  have  called  Hv,  the  "  head  on 

the  venturi."     Or  v*  =  the  velocity  through 

the  venturi, 

VQ  j         
—  \j2gHv=  I.OO62  ^2  g  Hv; 

where  the  first  supposition  has  supposed  v  i  =  y/2  g  Hv, 
abstracting  in  both  instances  from  the  co-efficients  for 
actual  use,  which  experiment  alone  can  supply. 


Builders  Iron  Foundry 

Founders  and  Machinists 


Gun  Iron  Air  Furnace  Castings 

Machinery  Castings 

Architectural  Iron  Work 

Pneumatic  Tubes  and  Caissons  for  Bridge  Piers 

Globe  Special  Castings  for  Water  Works 

The  Venturi  Meter 

Special  Machinery 

Fine  and  Heavy  Machine  Work 

Grinding  and  Polishing  Machinery 


Codding,  Westminster  and  Dodge  Streets, 

Providence,  R.  L 


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